Assignment 3 Solutions
1 a)
The following are the plots of the time series, ACF and PACF (of all the given data):
Figure : Scatter Plot for Whole Dataset
Figure : ACF and PACF Plots of Whole Dataset
One can see from the time series above that the data are not stationary. Rather, there
seems to be an increasing trend over time. The slow decay (nonexponential nature) of the ACF
plot and the spikes in the PACF plot indicate high autocorrelation between the lags of the time
series (from both the MA and AR components respectively). Thus, time series modelling is
required in order to account for these factors.
b)
By taking the natural logarithm of the data and differencing each datum with its previous lag
(except for the first point) on the training dataset
, the time series is detrended. This can be seen in
the following figure:
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View Full DocumentFigure : Plot of Detrended Time Series Data
The transformed data seem to both centre around zero and have constant variation. A suitable test
for stationarity would the Augmented DickeyFuller test where the null hypothesis assumes that
a unit root is present (i.e. the time series is nonstationary) as opposed to the alternate hypothesis
that a unit root is not present. The following is the RCode.
> library(tseries)
> adf.test(diff(log(tr_ISOL_RATE)))
Augmented DickeyFuller Test
data:
diff(log(tr_ISOL_RATE))
DickeyFuller = 7.3221, Lag order = 6, pvalue = 0.01
alternative hypothesis: stationary
Warning message:
In adf.test(diff(log(tr_ISOL_RATE))) : pvalue smaller than printed pvalue
Thus, with a pvalue smaller than 0.05, the null hypothesis is rejected and one concludes that the
transformed time series is stationary.
c)
The model used here was a SARIMA on the logarithmic values of the training dataset
.
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 Spring '09
 YuliaGel
 Statistics, Forecasting, Normal Distribution, Statistical hypothesis testing, ACF

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